Units and Measurement - Live session test

A cube has a numerically equal volume and surface area. The volume of such a cube is :
1. 216 units
2. 1000 units
3. 2000 units
4. 3000 units

Henry/ohm can be expressed in
(1) Second
(2) Coulomb
(3) Mho
(4) Metre

$E r g - m^{- 1}$ can be the unit of measure for
(1) Force
(2) Momentum
(3) Power
(4) Acceleration

Which of the following represents a volt :
(1) Joule/second
(2) Watt/Ampere
(3) Watt/Coulomb
(4) Coulomb/Joule

The unit of specific resistance is
(1) Ohm / cm²
(2) Ohm / cm
(3) Ohm - cm
(4) (Ohm - cm)^-1

Given the equation $\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}$. The units of $a$ will be: (where $P$ is pressure and $V$ is volume)
1. $\text{dyne} \times \text{cm}^5$
2. $\text{dyne} \times \text{cm}^4$
3. $\text{dyne} / \text{cm}^3$
4. $\text{dyne} / \text{cm}^2$

A physical quantity $A$ is related to four observable quantities $a$, $b$, $c$ and $d$ as follows, $A= \frac{a^2b^3}{c\sqrt{d}},$ the percentage errors of measurement in $a$, $b$, $c$ and $d$ are $1\%$, $3\%$, $2\%$ and $2\%$ respectively. The percentage error in quantity $A$ will be:
1. $12\%$
2. $7\%$
3. $5\%$
4. $14\%$

If the acceleration due to gravity is 10 ms^–2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is
(1) 360000
(2) 72,000
(3) 36,000
(4) 129600

The frequency of vibration of string is given by $ν = \frac{p}{2 l} {[\frac{F}{m}]}^{1 / 2}$ . Here p is number of segments in the string and l is the length. The dimensional formula for m will be
(1) $[M^{0} L T^{- 1}]$
(2) $[M L^{0} T^{- 1}]$
(3) $[M L^{- 1} T^{0}]$
(4) $[M^{0} L^{0} T^{0}]$

10. Given below are two statements:

Assertion (A):	Out of three measurements $l=0.7$ m; $l=0.70$ m and $l=0.700$ m, the last one is most accurate.
Reason (R):	In every measurement, only the last significant digit is not accurately known.

1.	Both (A) and (R) are True and (R) is the correct explanation of (A).
2.	Both (A) and (R) are True but (R) is not the correct explanation of (A).
3.	(A) is True but (R) is False.
4.	(A) is False but (R) is True.

11.

Assertion : In $y = A \sin (ω t - k x),$ $(ω t - k x)$ is dimensionless.
Reason : Because dimension of $ω = [M^{0} L^{0} T] .$

12.

Choose any one of the following four responses :
(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(3) If assertion is true but reason is false.
(4) If the assertion and reason both are false.
Assertion :The time period of a pendulum is given by the formula, $T = 2 π \sqrt{l / g}$ .
Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.

13.

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation $v = a t + \frac{b}{t + c}$ ; the dimensions of a, b and c are
(1) $a = L^{2}, b = T, c = L T^{2}$
(2) $a = L T^{2}, b = L T, c = L$
(3) $a = L T^{- 2}, b = L, c = T$
(4) $a = L, b = L T, c = T^{2}$

14.

The length, breadth, and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm The volume of the block according to the idea of significant figures should be:
(1) 1 × 10² cm³
(2) 2 × 10² cm³
(3) 1.764 × 10² cm³
(4) None of these

15.

If force (F), velocity (v) and time (T) are taken as fundamental units, then the dimensions of mass are
(1) [FvT^-1]
(2) [FvT^-2]
(3) [Fv^-1T^-1]
(4) [Fv^-1T]

16.

In certain vernier callipers, $25$ divisions on the vernier scale have the same length as $24$ divisions on the main scale. One division on the main scale is $1$ mm long. The least count of the instrument is:

1.	$0.04$ mm	2.	$0.01$ mm
3.	$0.02$ mm	4.	$0.08$ mm

17.

A Screw Guage gives the following readings when used to measure the diameter of a wire.
Main scale reading = 0.0 mm
Circular scale reading = 52 divisions
Given that: 1 mm on the main scale corresponds to 100 divisions of the circular scale.
The diameter of the wire from the above data is:
1. 0.026 cm
2. 0.005 cm
3. 0.52 cm
4. 0.052 cm

18.

Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?
It is given that the circular head translates $P$ MSD in ${N}$ rotations. ($1$ MSD $=$ $1~\text{mm}$.)

1. $ \left(\frac{{P}}{{N}}\right)\left(2+\frac{45}{100}\right) \text{mm} $
2. $ \left(\frac{{N}}{{P}}\right)\left(2+\frac{45}{{N}}\right) \text{mm} $
3. $P\left(\frac{2}{{N}}+\frac{45}{100}\right) \text{mm} $
4. $ \left(2+\frac{45}{100} \times \frac{{P}}{{N}}\right) \text{mm}$

19.

A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument? $1~\text{msd}= 100~\text{csd}=1~\text{mm}$

1.	$-0.16~\text{mm}$	2.	$+0.16~\text{mm}$
3.	$+0.14~\text{mm}$	4.	$-0.14~\text{mm}$

20.

Find the thickness of the wire. The least count is $0.01~\text{mm}$. The main scale reads (in mm):

1. $7.62$
2. $7.63$
3. $7.64$
4. $7.65$

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Assertion (A):	Out of three measurements \(l=0.7\) m; \(l=0.70\) m and \(l=0.700\) m, the last one is most accurate.
Reason (R):	In every measurement, only the last significant digit is not accurately known.

1.	\(-0.16~\text{mm}\)	2.	\(+0.16~\text{mm}\)
3.	\(+0.14~\text{mm}\)	4.	\(-0.14~\text{mm}\)

1.	\(0.04\) mm	2.	\(0.01\) mm
3.	\(0.02\) mm	4.	\(0.08\) mm

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